Precise Measurement and Formulation of Plastic Behaviour of Metals

In the present paper, results of investigations on the plastic behaviour under complex-loading by using an automatic complex-loading testing machine are summarized in accordance with the data obtained in our laboratory. Some experimental results on mild steel subjected to proportional deformations under combined loadings of axial force, torque and internal pressure applied to thin-walled tubular specimens with constant strain rate are discussed with emphasis on the effects of the first and third invariants of stress and strain. Experimental results under the above-mentioned combined loadings are discussed further on the plastic behaviour along the strain trajectories with a right-angle corner in the three-dimensional vector space corresponding to strain deviator. As the results of these experiments, the relations between stress and strain after the corner of strain trajectories which are in the relation of mirror transformation do not always agree with each other. However, such a disagreement for the relations almost vanishes after a modification in which the effect of the third invariant is eliminated from the experimental results. In other words, Ilyushin's "postulate of isotropy" is satisfied almost completely after such a modification on the results obtained by the above-mentioned experiments for mild steel. After such a modification, experimental relations between stress and strain after the corner of strain trajectory are formulated in a form of nonlinear tensor equality.